1. ## vectors

Is what im doing for la+bl correct?

2. $a+b = (4,-1,-3)
$

$|a+b| = \sqrt{4^2 + (-1)^2 + (-3)^2}$

3. No. |a + b| is not generally equal to |a| + |b|, although there are important relationships called the triangle inequality and the polarization identity relating the two expressions, and it is good to know the geometry of when they are equal.
You must first calculate the vector a + b by adding components, and then take the length |a + b| of that vector.